Child, Youth and Family (CYF) has mistakenly sent private details about a young woman to the wrong person, but says it is being blackmailed by the woman who received them.

CYF head Bernadine Mackenzie said the agency has taken legal action in relation to the Family Court document to protect the privacy of a young woman after the privacy breach.

"A mistake occurred and I'm sorry that our actions have seen a family's private information passed to a third party," she said.

"It should never have happened and we've apologised to the family for this. The family has been amazingly understanding of the mistake, and I thank them for that.

"Unfortunately, the woman who has this short document is refusing to return or destroy the information. She is demanding that we return one of her children to her care in exchange for the document."

Mackenzie said CYF had served the woman with an order from the Family Court prohibiting the publication of the information.

"With millions of interactions each day covering a huge proportion of the population, mistakes will happen despite the best of rules and processes," she said.

"We can't stop mistakes occurring but we are committed to fixing them, owning them and learning from them.

"This woman needs to do the right thing and think about the family whose information she is trying to hold to ransom."

Social Development Minister Paula Bennett said the agency had made a mistake, and that could not be overlooked.

"They have fronted up to it and they've apologised for it," she said. "But at the end of the day, someone can't try and blackmail the department to get them to give back their child when there are obviously reasons for that."

She said a short document was attached to other documents sent to a woman. CYF tried to retrieve that, realising its mistake, but the woman had refused to give it back.

"She is saying unless she gets her child back she will be going to the media and doing various other things.It is blackmail," Bennett said

The courts could order the information be retrieved.

The woman had a responsibility to give it back. It was information about a young person sent by human error, Bennett said.